Multi-dimensional unfolding is a procedure to recover positions of two
sets of points from a matrix of distances between the points of both
groups. For some of my research
work, I
implemented the algorithm for metric multi-dimensional unfolding that
Peter Schönemann published back in 1970 in
Psychometrika.
This is not the most advanced algorithm, however it is quite robust and
quick when a large number of points is involved. Note that it is an
algorithm for metric unfolding. That is, the input data need to be
interpretable as real distances.

The package that contains my implementation of Schönemann’s algorithm is
called munfold. It is now published on
CRAN. Development occurs
on GitHub, where both
releases and the
development tree can be found.

Figure 3: A demonstration of multidimensional unfolding. The left panel shows the
original configuration, the right panel shows the reconstructed
configuration. Note that the Schoenemann algorithm leads to a successful
reconstruction of the circle only if the positions of the points are
very slightly perturbed.¶